If you follow bhetghat's advice, you will be doing bhetghat with cops and immigration officers in a separate room for a very very long time.
Nepalese immigration officers ask for the proof that you are allowed to travel while departing or you entered in Nepal legally. If you show US passport during departure, they will ask for entry stamp/visa used during entry. Once they know you used Nepalese passport during entry, you are in a a big big problem. Nepalese constituion has not yet allowed dual citizenship.